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Demographics | Physical health | Hearing | Cognition | Mobility and balance | Quality of life | Mental health | Social participation and support | Views on hearing loss |


Background

Why impute missing data?

Logistic regression and other statistical methods require complete cases. In our case, with 40+ variables of interest, dropping participants with any missing values leads to a sample size of 200+ cases instead of 500+. There is loss of power, and estimates from models will likely be biased. The goal of missing data imputation is to restore variance of the sample to make it better reflect characteristics of the population (i.e., give accurate estimates of standard errors, CI’s, and p-values).

MICE procedure

‘Multiple Imputation by Chained Equations’

  1. Say there are three variables ‘A’, ‘B’, and ‘C’, each with some missing values. Choose variable ‘A’ to start filling in. Fill in missing values in ‘B’ and ‘C’ with temporary values, such as the mean.

  2. Make an equation A ~ B + C, using observed cases of ‘A’ to predict missing values of ‘A’, including a random component. Move on to predicting missing ‘B’, using B ~ A + C and including predicted ‘A’, again including a random component. Move on to predicting missing ‘C’, using C ~ A + B and predicted ‘A’ and ‘B’. This is one cycle.

  3. Choose the number of cycles, say 10 iterations. At the end of 10 iterations, an “imputed” dataset is formed with no missing values. Choose the number of imputed datasets to form (the same analysis will be conducted on each slightly different dataset, and the results will be pooled). Choose which variables should be used as predictors of other variables. Choose which method to use for predicting missing values, e.g., predictive mean matching. For derived variables such as summed scores, consider whether to impute components first and then calculate derived scores, or impute derived scores. Consider whether there should be an order of which variables to start imputing first.

  4. Check whether the imputed data “converge” (the means and SEs stabilize after a few iterations, and are similar across imputed datasets). Check the distributions and characteristics of imputed data (e.g. integer-only values, floors and ceilings, plausibility), and their similarity to observed data.


1. Pre-imputation work

(i) Evaluate missingness

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Variables of interest Demographics: Age, Gender, Work, Volunteer, Live alone
Physical health: Rating, Multimorbidity score, Subjective vision (loss, rating aided), Subjective hearing (loss, rating aided, rating unaided)
Hearing health: Hearing device use, Hearing device type, Tinnitus past 7 days, 15i-SSQ mean score, SIM mean score, EmoCheQ mean score, HHIE-S total score, BPTA4
Cognitive health: Subjective cognitive impairment, CSRQ mean score
Mobility and balance: Mobility aid use, ABC (balance confidence) mean score
Quality of life: SWLS mean score, WHO overall QoL, WHO health QoL, WHO money, WHO four domains
Mental health: PHQ4, split into anxiety and depression subscores
Social factors: Loneliness, Social Network Index, Social Participation Frequency, Social Participation Types, Social Support MOS mean score
Views: Connections total correct score, Motivations mean score
% Missing data within participants
## 
##   The decimal point is at the |
## 
##    0 | 00004444444444444444444444444444444444444999999999999999999999999999+193
##    2 | 22222222222222222222222222222222222222222277777777777777777777777777+16
##    4 | 000044444999993333333888888888888
##    6 | 222222222222222666666666666666666111111111111111111155555555555
##    8 | 0000000004444888833337777
##   10 | 221199
##   12 | 488
##   14 | 2055
##   16 | 47
##   18 | 65
##   20 | 
##   22 | 5
##   24 | 2
##   26 | 
##   28 | 
##   30 | 
##   32 | 
##   34 | 
##   36 | 
##   38 | 
##   40 | 
##   42 | 9
##   44 | 
##   46 | 
##   48 | 
##   50 | 
##   52 | 
##   54 | 
##   56 | 
##   58 | 
##   60 | 6
##   62 | 
##   64 | 6
##   66 | 87
##   68 | 
##   70 | 8827
##   72 | 6
##   74 | 337
##   76 | 0
##   78 | 
##   80 | 5
##   82 | 
##   84 | 
##   86 | 
##   88 | 
##   90 | 6
##   92 | 
##   94 | 
##   96 | 
##   98 | 66
Missing data patterns


Participants with <26% missing data (n=509):


Participants with >42% missing data (n=18):


(ii) Data cleaning

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Rules
  • For “single-item” variables (e.g. loneliness): NA’s are left as is.
  • For co-morbidity checklist: All responses other than “yes” (NA’s, No, Don’t know) are treated as “no”.
  • For composite variables: If a participant has “NA” for all items, the composite score is also “NA”.
  • WHOQOL-BREF: Follow their protocol for NA’s.
  • For SIM, EmoCheQ, CSRQ, PHQ4, Views on motivations: Impute case mean.
  • For 15i-SSQ: Impute case mean within subscale.
  • For HHIES: Impute case mode within subscale.
  • For ABC: Recode NA’s to 0 (single participant).
  • For Social Network Index: Recode NA’s to “never”.
  • For Social Participation: Recode NA’s to “never”.
  • For Social Support: Recode NA’s to “none”.
  • For Views (Connections): Drop foil item; only correct items credited.
  • For Views (Motivations): Impute mean.


Cleaning details


(iii) Evaluate missingness again

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% Missing data within participants
## 
##   The decimal point is at the |
## 
##    0 | 00000000000000000000000000000000000000000000000000000000000000000000+151
##    2 | 22222222222222222222222222222222222222222222222222222222222222222222+51
##    4 | 333333333333333333333333333333333333333333333
##    6 | 555555555555555555555555555555555555555555555555555555555
##    8 | 777777777777777777777777777
##   10 | 99999999999
##   12 | 00000
##   14 | 
##   16 | 4
##   18 | 6
##   20 | 
##   22 | 
##   24 | 
##   26 | 
##   28 | 
##   30 | 
##   32 | 
##   34 | 
##   36 | 
##   38 | 
##   40 | 3
##   42 | 
##   44 | 
##   46 | 
##   48 | 
##   50 | 0
##   52 | 22
##   54 | 3
##   56 | 
##   58 | 7777
##   60 | 999
##   62 | 
##   64 | 2
##   66 | 
##   68 | 6
##   70 | 7
##   72 | 
##   74 | 
##   76 | 1
##   78 | 
##   80 | 
##   82 | 
##   84 | 
##   86 | 
##   88 | 
##   90 | 33
Missing data patterns


Participants with <20% missing data (n=509):

## # A tibble: 45 × 3
##    variable                        n_miss pct_miss
##    <chr>                            <int>    <num>
##  1 Gender_bin                           0    0    
##  2 Age                                  2    0.393
##  3 Retired_bin                          0    0    
##  4 Volunteer                            0    0    
##  5 Lives_alone_bin                      0    0    
##  6 Phys_health_rating                   7    1.38 
##  7 Multimorbidity_score                 0    0    
##  8 Subj_vision_loss_bin                18    3.54 
##  9 Subj_vision_rating_aided             1    0.196
## 10 Subj_hearing_loss_bin               36    7.07 
## 11 any_hearing_device                   0    0    
## 12 study2_HA                            0    0    
## 13 Subj_hearing_rating_aided_REV      159   31.2  
## 14 Subj_hearing_rating_unaided_REV      8    1.57 
## 15 Tinnitus_past_wk_bin                 0    0    
## 16 ssq_speech_REV                      46    9.04 
## 17 ssq_spatial_REV                     51   10.0  
## 18 ssq_qualities_REV                    3    0.589
## 19 SIM_mean                            12    2.36 
## 20 Emocheq_mean                         8    1.57 
## 21 hhies_emo_total                      0    0    
## 22 hhies_soc_total                      0    0    
## 23 positive_SCI_bin                     0    0    
## 24 CSRQ_mean                            0    0    
## 25 Mobility_needs_bin                   0    0    
## 26 ABC_mean                             0    0    
## 27 SWLS_mean                            0    0    
## 28 WHOQOL_overall_qol                   0    0    
## 29 WHOQOL_health_qol                    0    0    
## 30 WHOQOL_Dom1_phys                     0    0    
## 31 WHOQOL_Dom2_psy                      0    0    
## 32 WHOQOL_Dom3_soc                      1    0.196
## 33 WHOQOL_Dom4_env                      0    0    
## 34 WHO_money                            0    0    
## 35 PHQ4_anx_sum                         1    0.196
## 36 PHQ4_dep_sum                         1    0.196
## 37 Lonely_bin                           1    0.196
## 38 Social_network_index                 1    0.196
## 39 Soc_part_freq                        1    0.196
## 40 Soc_part_types                       1    0.196
## 41 Socsupp_mean                         5    0.982
## 42 Connections_total                    9    1.77 
## 43 Motivate_mean                        5    0.982
## 44 study1_HA_bin                       78   15.3  
## 45 PTA4_better_ear                     73   14.3


Participants with >39%% missing data (n=18):


(iv) Justify discarding/retaining participants

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Drop 2 cases that are fully missing
##     Progress Duration.in.seconds Finished
## 458        0                 217        0
## 467        1                 540        0
## # A tibble: 46 × 3
##    variable                        n_miss pct_miss
##    <chr>                            <int>    <num>
##  1 Gender_bin                           2      100
##  2 Age                                  2      100
##  3 Retired_bin                          2      100
##  4 Volunteer                            2      100
##  5 Lives_alone_bin                      2      100
##  6 Phys_health_rating                   2      100
##  7 Multimorbidity_score                 0        0
##  8 Subj_vision_loss_bin                 2      100
##  9 Subj_vision_rating_aided             2      100
## 10 Subj_hearing_loss_bin                2      100
## 11 any_hearing_device                   0        0
## 12 study2_HA                            0        0
## 13 Subj_hearing_rating_aided_REV        2      100
## 14 Subj_hearing_rating_unaided_REV      2      100
## 15 Tinnitus_past_wk_bin                 0        0
## 16 ssq_speech_REV                       2      100
## 17 ssq_spatial_REV                      2      100
## 18 ssq_qualities_REV                    2      100
## 19 SIM_mean                             2      100
## 20 Emocheq_mean                         2      100
## 21 hhies_emo_total                      2      100
## 22 hhies_soc_total                      2      100
## 23 positive_SCI_bin                     2      100
## 24 CSRQ_mean                            2      100
## 25 Mobility_needs_bin                   2      100
## 26 ABC_mean                             2      100
## 27 SWLS_mean                            2      100
## 28 WHOQOL_overall_qol                   2      100
## 29 WHOQOL_health_qol                    2      100
## 30 WHOQOL_Dom1_phys                     2      100
## 31 WHOQOL_Dom2_psy                      2      100
## 32 WHOQOL_Dom3_soc                      2      100
## 33 WHOQOL_Dom4_env                      2      100
## 34 WHO_money                            2      100
## 35 PHQ4_anx_sum                         2      100
## 36 PHQ4_dep_sum                         2      100
## 37 Lonely_bin                           2      100
## 38 Social_network_index                 2      100
## 39 Soc_part_freq                        2      100
## 40 Soc_part_types                       2      100
## 41 Socsupp_mean                         2      100
## 42 Connections_total                    2      100
## 43 Motivate_mean                        2      100
## 44 study1_HA_bin                        2      100
## 45 PTA4_better_ear                      2      100
## 46 PTA4_asym                            2      100
Retain 16 that mostly have age, audiogram, earlier measures
##     Progress Duration.in.seconds Finished
## 45        58                 413        0
## 77        19                 247        0
## 136       58              308782        0
## 153       30                 449        0
## 166       52                 185        0
## 176       53                1693        0
## 187       53              518035        0
## 192       45              504174        0
## 228       13                  96        0
## 246       64                1719        0
## 318       55                 466        0
## 364       55                 988        0
## 405       55                 650        0
## 483       45                 731        0
## 520       64                6724        0
## 522       70                2376        0
## # A tibble: 46 × 3
##    variable                        n_miss pct_miss
##    <chr>                            <int>    <num>
##  1 Gender_bin                           0     0   
##  2 Age                                  1     6.25
##  3 Retired_bin                          0     0   
##  4 Volunteer                            0     0   
##  5 Lives_alone_bin                      0     0   
##  6 Phys_health_rating                   2    12.5 
##  7 Multimorbidity_score                 0     0   
##  8 Subj_vision_loss_bin                 2    12.5 
##  9 Subj_vision_rating_aided             2    12.5 
## 10 Subj_hearing_loss_bin                3    18.8 
## 11 any_hearing_device                   0     0   
## 12 study2_HA                            0     0   
## 13 Subj_hearing_rating_aided_REV        8    50   
## 14 Subj_hearing_rating_unaided_REV      3    18.8 
## 15 Tinnitus_past_wk_bin                 0     0   
## 16 ssq_speech_REV                      13    81.2 
## 17 ssq_spatial_REV                     11    68.8 
## 18 ssq_qualities_REV                    6    37.5 
## 19 SIM_mean                            11    68.8 
## 20 Emocheq_mean                        11    68.8 
## 21 hhies_emo_total                     13    81.2 
## 22 hhies_soc_total                     13    81.2 
## 23 positive_SCI_bin                    13    81.2 
## 24 CSRQ_mean                           15    93.8 
## 25 Mobility_needs_bin                  15    93.8 
## 26 ABC_mean                            15    93.8 
## 27 SWLS_mean                           15    93.8 
## 28 WHOQOL_overall_qol                  16   100   
## 29 WHOQOL_health_qol                   16   100   
## 30 WHOQOL_Dom1_phys                    16   100   
## 31 WHOQOL_Dom2_psy                     16   100   
## 32 WHOQOL_Dom3_soc                     16   100   
## 33 WHOQOL_Dom4_env                     16   100   
## 34 WHO_money                           16   100   
## 35 PHQ4_anx_sum                        16   100   
## 36 PHQ4_dep_sum                        16   100   
## 37 Lonely_bin                          16   100   
## 38 Social_network_index                16   100   
## 39 Soc_part_freq                       16   100   
## 40 Soc_part_types                      16   100   
## 41 Socsupp_mean                        16   100   
## 42 Connections_total                   16   100   
## 43 Motivate_mean                       16   100   
## 44 study1_HA_bin                        3    18.8 
## 45 PTA4_better_ear                      3    18.8 
## 46 PTA4_asym                            3    18.8


(v) Variable relationships

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Correlations heatmap: Hearing

Correlations heatmap: Physical health
PCA

Note: PC1 and PC2 account for 36% of the total variance.



2. Imputation using MICE

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Current method

  • Use predictors that correlate 0.5 or better to impute missing data in a variable (30 variables); if no such predictors, adjust threshold to 0.4 (3 variables), then 0.3, then 0.2 (2 variables)
    pdf
  • Eight variables are complete and do not require imputing; 2 variables have no predictors that correlate at least r = 0.2 (Subj_vision_loss_bin, Connections_total)
  • MICE settings: total of 5 imputed datasets, with a maximum of 10 iterations per dataset, using predictive means matching to impute missing values

Check imputed data

  • Convergence
    pdf

  • Compare imputed to observed data
    pdf

  • Characteristics of imputed data
    pdf

PCA with standardized imputed data

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PCA

Note: This is only 1 of 5 imputed datasets, but the plots are similar.



3. Predicting hearing aid adoption

Complete cases vs. imputed data

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Note: All participants together; not filtered by hearing aid candidacy.

Regression output (complete cases, n=346)

Non-hearing aid users = 267
Hearing aid users = 79 (22.8%)
Note: Dropped Subj_hearing_rating_aided_REV & SWLS_mean due to VIF > 5


##                               Term Estimate StdError       z      p     OddsRatio CIlower CIupper
## 1                      (Intercept) -24.2964 884.2360 -0.0275 0.9781        0.0000  0.0000     Inf
## 2                       Gender_bin   0.5265   0.4564  1.1536 0.2487        1.6930  0.6921  4.1418
## 3                              Age  -0.0185   0.0346 -0.5336 0.5936        0.9817  0.9172  1.0506
## 4                      Retired_bin   0.0571   0.5098  0.1121 0.9108        1.0588  0.3898  2.8757
## 5                    Volunteer_rec   0.5477   0.2816  1.9448 0.0518        1.7293  0.9957  3.0031
## 6                  Lives_alone_bin  -0.2751   0.5566 -0.4943 0.6211        0.7595  0.2551  2.2608
## 7               Phys_health_rating   0.0966   0.3728  0.2590 0.7956        1.1014  0.5304  2.2868
## 8             Multimorbidity_score  -0.0199   0.1206 -0.1652 0.8688        0.9803  0.7739  1.2417
## 9               Mobility_needs_bin  -0.3204   1.1148 -0.2874 0.7738        0.7258  0.0816  6.4536
## 10                        ABC_mean  -0.0315   0.0261 -1.2055 0.2280        0.9690  0.9206  1.0199
## 11        Subj_vision_rating_aided   0.0508   0.2960  0.1717 0.8637        1.0521  0.5890  1.8795
## 12           Subj_hearing_loss_bin  17.0709 884.2210  0.0193 0.9846 25929968.0135  0.0000     Inf
## 13 Subj_hearing_rating_unaided_REV   1.0591   0.3850  2.7506 0.0059        2.8837  1.3559  6.1334
## 14            Tinnitus_past_wk_bin   0.1555   0.4104  0.3790 0.7047        1.1683  0.5227  2.6112
## 15                 PTA4_better_ear   0.1214   0.0288  4.2225 0.0000        1.1291  1.0672  1.1945
## 16                       PTA4_asym   0.0472   0.0153  3.0891 0.0020        1.0483  1.0174  1.0802
## 17                 SSQ15i_mean_REV  -0.6680   0.1855 -3.6002 0.0003        0.5128  0.3564  0.7376
## 18                    Emocheq_mean  -0.0308   0.2780 -0.1108 0.9118        0.9697  0.5623  1.6721
## 19                     HHIES_total   0.0596   0.0386  1.5445 0.1225        1.0614  0.9841  1.1448
## 20                        SIM_mean  -0.1358   0.1165 -1.1662 0.2435        0.8730  0.6948  1.0968
## 21                positive_SCI_bin   1.1976   0.7118  1.6824 0.0925        3.3122  0.8207 13.3674
## 22                       CSRQ_mean  -0.1344   0.6195 -0.2170 0.8282        0.8742  0.2596  2.9440
## 23                    PHQ4_anx_sum   0.7501   0.2500  3.0009 0.0027        2.1173  1.2972  3.4559
## 24                    PHQ4_dep_sum  -0.5725   0.3340 -1.7137 0.0866        0.5641  0.2931  1.0857
## 25              WHOQOL_overall_qol  -0.4355   0.4717 -0.9233 0.3558        0.6469  0.2567  1.6306
## 26               WHOQOL_health_qol   0.3760   0.3228  1.1648 0.2441        1.4565  0.7736  2.7421
## 27                       WHO_money   0.8039   0.2691  2.9869 0.0028        2.2343  1.3184  3.7865
## 28                    Socsupp_mean   0.2161   0.2994  0.7216 0.4705        1.2412  0.6902  2.2320
## 29            Social_network_index  -0.1362   0.1756 -0.7754 0.4381        0.8727  0.6185  1.2313
## 30                   Soc_part_freq  -0.2681   0.3671 -0.7303 0.4652        0.7648  0.3724  1.5706
## 31                  Soc_part_types   0.0183   0.1582  0.1155 0.9080        1.0184  0.7469  1.3886
## 32                      Lonely_bin  -0.2511   0.6864 -0.3658 0.7145        0.7780  0.2026  2.9868
## 33                   Motivate_mean   0.3051   0.2395  1.2743 0.2026        1.3568  0.8486  2.1694
Regression output (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -0.6403   0.3616 -1.7705 234.2875 0.0779    0.5271  0.2595  1.0708
## 2                       Gender_bin   0.0567   0.0364  1.5575 471.1834 0.1200    1.0583  0.9855  1.1366
## 3                              Age   0.0025   0.0025  0.9825 369.2798 0.3265    1.0025  0.9976  1.0074
## 4                      Retired_bin  -0.0293   0.0369 -0.7938 487.6629 0.4277    0.9711  0.9034  1.0440
## 5                    Volunteer_rec   0.0426   0.0207  2.0563 446.2648 0.0403    1.0435  1.0020  1.0867
## 6                  Lives_alone_bin  -0.0218   0.0421 -0.5181 456.7222 0.6047    0.9784  0.9009  1.0626
## 7               Phys_health_rating  -0.0025   0.0275 -0.0922 277.7467 0.9266    0.9975  0.9452  1.0527
## 8             Multimorbidity_score   0.0044   0.0077  0.5739 482.4389 0.5663    1.0044  0.9894  1.0197
## 9               Mobility_needs_bin  -0.0263   0.0882 -0.2982 197.5034 0.7658    0.9740  0.8194  1.1579
## 10                        ABC_mean  -0.0032   0.0017 -1.9082 333.4289 0.0572    0.9968  0.9935  1.0001
## 11        Subj_vision_rating_aided   0.0101   0.0234  0.4302 464.5342 0.6672    1.0102  0.9649  1.0576
## 12           Subj_hearing_loss_bin   0.0965   0.0509  1.8948 251.8043 0.0593    1.1013  0.9967  1.2168
## 13 Subj_hearing_rating_unaided_REV   0.0970   0.0253  3.8375 474.5172 0.0001    1.1019  1.0486  1.1579
## 14            Tinnitus_past_wk_bin  -0.0538   0.0348 -1.5461 477.2992 0.1227    0.9476  0.8851  1.0145
## 15                 PTA4_better_ear   0.0077   0.0023  3.2957  65.6229 0.0016    1.0077  1.0032  1.0123
## 16                       PTA4_asym   0.0028   0.0015  1.8521  97.2075 0.0670    1.0028  0.9999  1.0058
## 17                 SSQ15i_mean_REV  -0.0682   0.0134 -5.0841 442.5085 0.0000    0.9341  0.9099  0.9589
## 18                    Emocheq_mean  -0.0047   0.0218 -0.2154 308.9247 0.8296    0.9953  0.9537  1.0388
## 19                     HHIES_total   0.0063   0.0031  2.0680 139.2159 0.0405    1.0063  1.0002  1.0125
## 20                        SIM_mean  -0.0037   0.0086 -0.4296 151.3338 0.6681    0.9963  0.9797  1.0132
## 21                positive_SCI_bin   0.0444   0.0597  0.7437 235.7357 0.4578    1.0454  0.9300  1.1752
## 22                       CSRQ_mean  -0.0471   0.0504 -0.9332 237.7601 0.3517    0.9540  0.8643  1.0530
## 23                    PHQ4_anx_sum   0.0590   0.0189  3.1289 349.5162 0.0019    1.0608  1.0222  1.1008
## 24                    PHQ4_dep_sum  -0.0048   0.0219 -0.2174 410.0640 0.8280    0.9952  0.9534  1.0389
## 25              WHOQOL_overall_qol   0.0215   0.0338  0.6349 399.5565 0.5258    1.0217  0.9562  1.0917
## 26               WHOQOL_health_qol   0.0263   0.0239  1.0977 242.7875 0.2734    1.0266  0.9797  1.0759
## 27                       WHO_money   0.0327   0.0191  1.7141 379.8742 0.0873    1.0332  0.9953  1.0727
## 28                    Socsupp_mean   0.0121   0.0242  0.5018 257.1651 0.6163    1.0122  0.9653  1.0613
## 29            Social_network_index  -0.0035   0.0143 -0.2440 257.7509 0.8074    0.9965  0.9690  1.0248
## 30                   Soc_part_freq   0.0044   0.0285  0.1553 277.8290 0.8767    1.0044  0.9498  1.0621
## 31                  Soc_part_types  -0.0052   0.0132 -0.3953 230.6520 0.6930    0.9948  0.9694  1.0209
## 32                      Lonely_bin  -0.0036   0.0491 -0.0739 243.8208 0.9412    0.9964  0.9050  1.0971
## 33                   Motivate_mean   0.0172   0.0208  0.8254 197.5883 0.4101    1.0173  0.9767  1.0597


Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]


Accuracy of model predictions

Note: Not really a fair comparison as models and model coefficients are different between complete-cases and imputed data.

## [1] "Complete cases, using median as boundary"
##       predicted
## actual   0   1
##      0 170  97
##      1   3  76
## [1] "Accuracy: 0.711"
## [1] "Sensitivity: 0.962"
## [1] "Specificity: 0.637"

## [1] "Imputed data, using median as boundary"
##       predicted
## actual   0   1
##      0 255 167
##      1   8  95
## [1] "Accuracy: 0.667"
## [1] "Sensitivity: 0.922"
## [1] "Specificity: 0.604"


Grouping by HHIE-S status

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Counts

0-8 no handicap, 10-24 mild to moderate, 26-40 severe

##       HHIES
## UseHA  None MildMod Sev <NA>
##   0     233     148  30   11
##   1      26      62  13    2
##   <NA>    0       0   0    0
## [1] 0.100 0.295 0.302 0.154
Regression output (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)   0.1962   0.4650  0.4219 183.5297 0.6736    1.2168  0.4891  3.0271
## 2                       Gender_bin  -0.0326   0.0425 -0.7671 223.1006 0.4438    0.9679  0.8906  1.0520
## 3                              Age  -0.0003   0.0030 -0.0861 195.9337 0.9315    0.9997  0.9938  1.0056
## 4                      Retired_bin  -0.0200   0.0414 -0.4817 220.3576 0.6305    0.9802  0.9038  1.0631
## 5                    Volunteer_rec   0.0331   0.0231  1.4306 220.6900 0.1540    1.0337  0.9879  1.0815
## 6                  Lives_alone_bin   0.0398   0.0462  0.8608 221.0689 0.3903    1.0406  0.9505  1.1392
## 7               Phys_health_rating  -0.0295   0.0316 -0.9348 215.7359 0.3510    0.9709  0.9126  1.0330
## 8             Multimorbidity_score   0.0100   0.0112  0.8962 221.7392 0.3711    1.0101  0.9881  1.0325
## 9               Mobility_needs_bin   0.0198   0.1146  0.1728 214.7225 0.8630    1.0200  0.8148  1.2769
## 10                        ABC_mean  -0.0013   0.0026 -0.5184 223.0057 0.6047    0.9987  0.9936  1.0038
## 11        Subj_vision_rating_aided  -0.0231   0.0283 -0.8162 218.0165 0.4153    0.9772  0.9244  1.0329
## 12           Subj_hearing_loss_bin   0.0905   0.0500  1.8105 221.0717 0.0716    1.0947  0.9925  1.2074
## 13 Subj_hearing_rating_unaided_REV   0.0481   0.0293  1.6414 202.2892 0.1023    1.0493  0.9907  1.1113
## 14            Tinnitus_past_wk_bin  -0.0516   0.0426 -1.2121 221.3916 0.2268    0.9497  0.8736  1.0324
## 15                 PTA4_better_ear   0.0096   0.0029  3.3415 105.5930 0.0012    1.0096  1.0039  1.0154
## 16                       PTA4_asym   0.0043   0.0033  1.2813  29.2730 0.2101    1.0043  0.9978  1.0108
## 17                 SSQ15i_mean_REV  -0.0507   0.0202 -2.5136 138.4644 0.0131    0.9506  0.9137  0.9890
## 18                    Emocheq_mean  -0.0076   0.0287 -0.2650 220.7188 0.7912    0.9924  0.9381  1.0499
## 19                     HHIES_total   0.0042   0.0075  0.5613 219.0136 0.5752    1.0042  0.9896  1.0191
## 20                        SIM_mean   0.0027   0.0094  0.2892 204.2855 0.7727    1.0027  0.9844  1.0213
## 21                positive_SCI_bin   0.1466   0.1061  1.3813 179.7737 0.1689    1.1579  0.9405  1.4255
## 22                       CSRQ_mean  -0.0401   0.0542 -0.7396 220.0602 0.4604    0.9607  0.8639  1.0684
## 23                    PHQ4_anx_sum   0.0506   0.0232  2.1797 215.4355 0.0304    1.0519  1.0051  1.1008
## 24                    PHQ4_dep_sum  -0.0408   0.0310 -1.3165 190.7873 0.1896    0.9600  0.9034  1.0202
## 25              WHOQOL_overall_qol  -0.0135   0.0396 -0.3407 171.3142 0.7337    0.9866  0.9129  1.0662
## 26               WHOQOL_health_qol   0.0028   0.0274  0.1014 202.5631 0.9194    1.0028  0.9504  1.0581
## 27                       WHO_money   0.0439   0.0236  1.8571 222.3120 0.0646    1.0449  0.9976  1.0943
## 28                    Socsupp_mean   0.0170   0.0288  0.5880 215.9515 0.5571    1.0171  0.9613  1.0762
## 29            Social_network_index  -0.0099   0.0154 -0.6473 222.8188 0.5181    0.9901  0.9607  1.0205
## 30                   Soc_part_freq  -0.0143   0.0339 -0.4212 196.6811 0.6741    0.9858  0.9224  1.0535
## 31                  Soc_part_types  -0.0069   0.0142 -0.4865 211.1557 0.6271    0.9931  0.9659  1.0212
## 32                      Lonely_bin  -0.0189   0.0621 -0.3040 215.3301 0.7614    0.9813  0.8688  1.1083
## 33                   Motivate_mean  -0.0219   0.0236 -0.9279 218.4380 0.3545    0.9783  0.9341  1.0247
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -1.3733   0.5989 -2.2930 124.8454 0.0235    0.2533  0.0783  0.8192
## 2                       Gender_bin   0.1154   0.0656  1.7607 190.4086 0.0799    1.1223  0.9869  1.2763
## 3                              Age   0.0054   0.0045  1.2010 125.0713 0.2320    1.0054  0.9966  1.0143
## 4                      Retired_bin  -0.0564   0.0660 -0.8549 216.5146 0.3935    0.9452  0.8305  1.0757
## 5                    Volunteer_rec   0.0408   0.0371  1.0988 217.2892 0.2731    1.0416  0.9686  1.1202
## 6                  Lives_alone_bin  -0.1349   0.0773 -1.7448 211.4367 0.0825    0.8738  0.7510  1.0167
## 7               Phys_health_rating   0.0197   0.0460  0.4289 210.2493 0.6684    1.0199  0.9320  1.1161
## 8             Multimorbidity_score   0.0002   0.0114  0.0206 208.7751 0.9836    1.0002  0.9781  1.0228
## 9               Mobility_needs_bin  -0.0130   0.1352 -0.0960 112.4445 0.9237    0.9871  0.7573  1.2866
## 10                        ABC_mean  -0.0046   0.0023 -1.9717 197.9761 0.0500    0.9954  0.9909  0.9999
## 11        Subj_vision_rating_aided   0.0372   0.0383  0.9706 210.7444 0.3329    1.0379  0.9628  1.1188
## 12           Subj_hearing_loss_bin   0.0967   0.1113  0.8688 159.3392 0.3863    1.1015  0.8856  1.3701
## 13 Subj_hearing_rating_unaided_REV   0.1389   0.0459  3.0292 200.1503 0.0028    1.1490  1.0502  1.2572
## 14            Tinnitus_past_wk_bin  -0.0386   0.0560 -0.6891 206.9787 0.4916    0.9621  0.8621  1.0738
## 15                 PTA4_better_ear   0.0088   0.0040  2.2120  27.0475 0.0356    1.0088  1.0010  1.0168
## 16                       PTA4_asym   0.0027   0.0022  1.2168  33.9089 0.2321    1.0027  0.9984  1.0070
## 17                 SSQ15i_mean_REV  -0.0734   0.0198 -3.7135 211.7069 0.0003    0.9292  0.8939  0.9660
## 18                    Emocheq_mean   0.0082   0.0330  0.2473 214.0387 0.8049    1.0082  0.9451  1.0756
## 19                     HHIES_total   0.0035   0.0054  0.6527 154.0751 0.5149    1.0035  0.9929  1.0142
## 20                        SIM_mean  -0.0196   0.0140 -1.4068 206.5296 0.1610    0.9806  0.9540  1.0079
## 21                positive_SCI_bin   0.0844   0.0836  1.0101 209.2780 0.3136    1.0881  0.9236  1.2818
## 22                       CSRQ_mean  -0.0339   0.0962 -0.3524  92.2837 0.7253    0.9667  0.8006  1.1673
## 23                    PHQ4_anx_sum   0.0446   0.0314  1.4199 185.7922 0.1573    1.0456  0.9832  1.1120
## 24                    PHQ4_dep_sum   0.0244   0.0330  0.7400 199.5112 0.4602    1.0247  0.9605  1.0932
## 25              WHOQOL_overall_qol   0.0633   0.0622  1.0167 118.1008 0.3114    1.0653  0.9431  1.2035
## 26               WHOQOL_health_qol   0.0390   0.0406  0.9619 206.9667 0.3372    1.0398  0.9602  1.1259
## 27                       WHO_money   0.0225   0.0320  0.7029 109.8648 0.4836    1.0228  0.9606  1.0890
## 28                    Socsupp_mean  -0.0189   0.0403 -0.4681 167.3214 0.6403    0.9813  0.9068  1.0619
## 29            Social_network_index   0.0012   0.0244  0.0511 212.3747 0.9593    1.0012  0.9544  1.0502
## 30                   Soc_part_freq   0.0246   0.0472  0.5210 142.3688 0.6032    1.0249  0.9343  1.1242
## 31                  Soc_part_types  -0.0020   0.0234 -0.0849 199.9804 0.9324    0.9980  0.9533  1.0448
## 32                      Lonely_bin   0.0211   0.0788  0.2681 206.1755 0.7889    1.0213  0.8752  1.1919
## 33                   Motivate_mean   0.0712   0.0364  1.9567 172.9059 0.0520    1.0738  0.9999  1.1532


Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]


Grouping by vision status

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Counts
## 
##    0    1 <NA> 
##  215  290   20
Regression output (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -0.3066   0.5791 -0.5295 176.5355 0.5971    0.7359  0.2365  2.2897
## 2                       Gender_bin   0.0271   0.0511  0.5301 174.6973 0.5967    1.0275  0.9295  1.1357
## 3                              Age  -0.0015   0.0040 -0.3808 133.1376 0.7039    0.9985  0.9907  1.0064
## 4                      Retired_bin  -0.0385   0.0539 -0.7141 178.9783 0.4761    0.9622  0.8658  1.0694
## 5                    Volunteer_rec   0.0678   0.0296  2.2906 170.0660 0.0232    1.0702  1.0098  1.1341
## 6                  Lives_alone_bin  -0.1206   0.0628 -1.9213 177.4447 0.0563    0.8864  0.7837  1.0025
## 7               Phys_health_rating  -0.0323   0.0401 -0.8052 175.6176 0.4218    0.9682  0.8950  1.0474
## 8             Multimorbidity_score   0.0166   0.0139  1.1934 179.3487 0.2343    1.0167  0.9894  1.0448
## 9               Mobility_needs_bin  -0.0900   0.1325 -0.6796 178.8050 0.4976    0.9139  0.7049  1.1849
## 10                        ABC_mean  -0.0048   0.0033 -1.4297 178.4190 0.1545    0.9952  0.9888  1.0017
## 11        Subj_vision_rating_aided   0.0062   0.0366  0.1698 177.8689 0.8654    1.0062  0.9366  1.0811
## 12           Subj_hearing_loss_bin   0.0965   0.0744  1.2966 110.8065 0.1975    1.1013  0.9519  1.2742
## 13 Subj_hearing_rating_unaided_REV   0.0246   0.0383  0.6438 171.5901 0.5206    1.0249  0.9508  1.1048
## 14            Tinnitus_past_wk_bin  -0.0340   0.0559 -0.6071 152.2968 0.5447    0.9666  0.8663  1.0785
## 15                 PTA4_better_ear   0.0096   0.0039  2.4399  19.4762 0.0244    1.0096  1.0020  1.0174
## 16                       PTA4_asym   0.0037   0.0021  1.8075 176.0733 0.0724    1.0037  0.9996  1.0078
## 17                 SSQ15i_mean_REV  -0.0512   0.0212 -2.4180 179.0185 0.0166    0.9501  0.9114  0.9904
## 18                    Emocheq_mean   0.0014   0.0336  0.0404 157.1019 0.9678    1.0014  0.9376  1.0696
## 19                     HHIES_total   0.0091   0.0046  1.9563 162.4779 0.0521    1.0091  1.0001  1.0183
## 20                        SIM_mean   0.0042   0.0116  0.3646 176.8644 0.7158    1.0042  0.9816  1.0273
## 21                positive_SCI_bin  -0.0876   0.0984 -0.8899 155.3114 0.3749    0.9161  0.7554  1.1110
## 22                       CSRQ_mean  -0.0522   0.0741 -0.7045 136.3395 0.4823    0.9491  0.8208  1.0975
## 23                    PHQ4_anx_sum   0.0509   0.0274  1.8535 176.7850 0.0655    1.0522  0.9972  1.1103
## 24                    PHQ4_dep_sum  -0.0102   0.0361 -0.2822 165.1584 0.7782    0.9899  0.9222  1.0624
## 25              WHOQOL_overall_qol   0.0134   0.0509  0.2627 179.1511 0.7931    1.0135  0.9173  1.1198
## 26               WHOQOL_health_qol   0.0631   0.0353  1.7871 172.9118 0.0757    1.0651  0.9939  1.1414
## 27                       WHO_money   0.0271   0.0272  0.9964 175.6697 0.3204    1.0275  0.9741  1.0837
## 28                    Socsupp_mean   0.0288   0.0344  0.8394 155.6949 0.4025    1.0292  0.9621  1.1010
## 29            Social_network_index   0.0002   0.0197  0.0086 178.5648 0.9932    1.0002  0.9623  1.0396
## 30                   Soc_part_freq   0.0695   0.0438  1.5855 161.6031 0.1148    1.0720  0.9838  1.1681
## 31                  Soc_part_types  -0.0153   0.0193 -0.7958 164.2810 0.4273    0.9848  0.9483  1.0228
## 32                      Lonely_bin  -0.0044   0.0751 -0.0585 148.1629 0.9534    0.9956  0.8593  1.1535
## 33                   Motivate_mean  -0.0059   0.0292 -0.2026 179.3079 0.8397    0.9941  0.9388  1.0527
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -1.2882   0.4977 -2.5882 122.9981 0.0108    0.2758  0.1040  0.7315
## 2                       Gender_bin   0.1151   0.0557  2.0671 196.7062 0.0400    1.1220  1.0059  1.2514
## 3                              Age   0.0067   0.0036  1.8643 239.4622 0.0635    1.0067  0.9996  1.0139
## 4                      Retired_bin  -0.0494   0.0519 -0.9516 248.3566 0.3422    0.9518  0.8597  1.0537
## 5                    Volunteer_rec   0.0371   0.0302  1.2278 244.5447 0.2207    1.0378  0.9782  1.1011
## 6                  Lives_alone_bin   0.0762   0.0609  1.2519 209.9147 0.2120    1.0792  0.9578  1.2160
## 7               Phys_health_rating   0.0279   0.0380  0.7341 154.8735 0.4640    1.0283  0.9545  1.1078
## 8             Multimorbidity_score  -0.0054   0.0097 -0.5506 252.4999 0.5824    0.9946  0.9759  1.0137
## 9               Mobility_needs_bin   0.0265   0.1215  0.2178 114.6821 0.8280    1.0269  0.8093  1.3030
## 10                        ABC_mean  -0.0021   0.0021 -1.0394 165.3739 0.3001    0.9979  0.9938  1.0020
## 11        Subj_vision_rating_aided   0.0013   0.0326  0.0402 248.4262 0.9680    1.0013  0.9393  1.0674
## 12           Subj_hearing_loss_bin   0.0739   0.0719  1.0273 170.9803 0.3057    1.0767  0.9352  1.2396
## 13 Subj_hearing_rating_unaided_REV   0.1157   0.0348  3.3203 252.0340 0.0010    1.1227  1.0486  1.2019
## 14            Tinnitus_past_wk_bin  -0.0472   0.0475 -0.9927 249.0090 0.3218    0.9539  0.8691  1.0470
## 15                 PTA4_better_ear   0.0066   0.0031  2.1441  93.3090 0.0346    1.0066  1.0005  1.0128
## 16                       PTA4_asym   0.0018   0.0021  0.8423 112.5263 0.4014    1.0018  0.9977  1.0059
## 17                 SSQ15i_mean_REV  -0.1002   0.0187 -5.3719 177.3916 0.0000    0.9047  0.8721  0.9384
## 18                    Emocheq_mean  -0.0066   0.0293 -0.2237 163.6258 0.8233    0.9934  0.9380  1.0521
## 19                     HHIES_total   0.0091   0.0040  2.2537 120.3900 0.0260    1.0091  1.0013  1.0171
## 20                        SIM_mean  -0.0117   0.0117 -1.0071 175.5777 0.3153    0.9884  0.9660  1.0113
## 21                positive_SCI_bin   0.0940   0.0773  1.2161 168.2063 0.2257    1.0986  0.9441  1.2783
## 22                       CSRQ_mean   0.0430   0.0735  0.5850 104.3475 0.5598    1.0439  0.9039  1.2057
## 23                    PHQ4_anx_sum   0.0777   0.0266  2.9170 166.8885 0.0040    1.0808  1.0259  1.1386
## 24                    PHQ4_dep_sum  -0.0134   0.0290 -0.4629 218.1068 0.6439    0.9867  0.9322  1.0444
## 25              WHOQOL_overall_qol   0.0869   0.0484  1.7932 208.3303 0.0744    1.0908  0.9921  1.1993
## 26               WHOQOL_health_qol   0.0135   0.0328  0.4127 168.1729 0.6804    1.0136  0.9505  1.0809
## 27                       WHO_money   0.0239   0.0275  0.8685 171.4992 0.3863    1.0242  0.9704  1.0809
## 28                    Socsupp_mean  -0.0029   0.0395 -0.0741  63.1461 0.9411    0.9971  0.9228  1.0774
## 29            Social_network_index   0.0029   0.0211  0.1364 139.3696 0.8917    1.0029  0.9623  1.0452
## 30                   Soc_part_freq  -0.0405   0.0401 -1.0112 165.2686 0.3134    0.9603  0.8877  1.0388
## 31                  Soc_part_types   0.0019   0.0190  0.1000 124.3464 0.9205    1.0019  0.9653  1.0399
## 32                      Lonely_bin  -0.0338   0.0690 -0.4899 152.5273 0.6249    0.9668  0.8445  1.1068
## 33                   Motivate_mean   0.0204   0.0309  0.6608  77.3440 0.5107    1.0206  0.9606  1.0843


Legend: Asterisks denote p < 0.05; crosses denote p [0.05, 0.1]


Variable selection: Predicting HA adoption

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Penalized logistic regression (LASSO) with 5-fold cross-validation was conducted across 100 lambda (penalty) values. The lambda value that led to the best-fitting model (with lowest cross-validation error) was 0.044, which corresponds to a model with 13 predictors:

Regression output (13 selected) (imputed data, n=525)
##                               Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                      (Intercept)  -0.7963   0.1793 -4.4423 466.5515 0.0000    0.4510  0.3174  0.6409
## 2                       Gender_bin   0.0355   0.0325  1.0917 489.3016 0.2755    1.0361  0.9722  1.1043
## 3                              Age   0.0022   0.0022  1.0205 290.7249 0.3083    1.0022  0.9979  1.0065
## 4                    Volunteer_rec   0.0421   0.0182  2.3067 472.5371 0.0215    1.0430  1.0064  1.0809
## 5                  Lives_alone_bin  -0.0225   0.0390 -0.5760 497.0567 0.5649    0.9778  0.9058  1.0554
## 6            Subj_hearing_loss_bin   0.0784   0.0482  1.6269 292.9549 0.1048    1.0816  0.9841  1.1887
## 7  Subj_hearing_rating_unaided_REV   0.0945   0.0244  3.8755 431.6994 0.0001    1.0991  1.0478  1.1530
## 8                  PTA4_better_ear   0.0083   0.0023  3.6810  67.2129 0.0005    1.0083  1.0038  1.0129
## 9                        PTA4_asym   0.0031   0.0014  2.1174 138.5066 0.0360    1.0031  1.0004  1.0059
## 10                 SSQ15i_mean_REV  -0.0749   0.0123 -6.0967 272.3709 0.0000    0.9278  0.9057  0.9505
## 11                     HHIES_total   0.0054   0.0025  2.1303 169.9426 0.0346    1.0054  1.0005  1.0104
## 12                    PHQ4_anx_sum   0.0480   0.0146  3.2757 187.7804 0.0013    1.0492  1.0196  1.0796
## 13                       WHO_money   0.0381   0.0178  2.1395 215.4898 0.0335    1.0388  1.0032  1.0757
## 14                    Socsupp_mean   0.0268   0.0208  1.2879 333.0934 0.1987    1.0272  0.9861  1.0699


Limiting the model to the 8 predictors with p < 0.05, all 8 predictors remain significant in a standard logistic regression model.

Regression output (8 selected) (imputed data, n=525)
##                              Term Estimate StdError       t       df      p OddsRatio CIlower CIupper
## 1                     (Intercept)  -0.6127   0.1044 -5.8707 218.5124 0.0000    0.5419  0.4416  0.6649
## 2                   Volunteer_rec   0.0421   0.0181  2.3210 428.5667 0.0208    1.0430  1.0066  1.0807
## 3 Subj_hearing_rating_unaided_REV   0.1115   0.0225  4.9617 379.4792 0.0000    1.1180  1.0697  1.1684
## 4                 PTA4_better_ear   0.0104   0.0018  5.6517 192.1114 0.0000    1.0105  1.0069  1.0140
## 5                       PTA4_asym   0.0034   0.0014  2.4128 206.3060 0.0167    1.0034  1.0007  1.0062
## 6                 SSQ15i_mean_REV  -0.0755   0.0123 -6.1393 279.6360 0.0000    0.9273  0.9052  0.9499
## 7                     HHIES_total   0.0054   0.0025  2.1268 130.9653 0.0353    1.0054  1.0005  1.0104
## 8                    PHQ4_anx_sum   0.0418   0.0145  2.8772 157.7745 0.0046    1.0427  1.0135  1.0727
## 9                       WHO_money   0.0509   0.0170  2.9949 226.0709 0.0031    1.0522  1.0177  1.0879



Accuracy of model predictions

## [1] "Imputed data, 8 predictors, using median as boundary to classify 0 or 1"
##       predicted
## actual   0   1
##      0 252 170
##      1  11  92
## [1] "Accuracy: 0.655"
## [1] "Sensitivity: 0.893"
## [1] "Specificity: 0.597"


ROC: BPTA4 and HA adoption

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Complete cases only (n=449)
Imputed data (n=525)
##   m best_threshold sensitivity specificity       auc
## 1 1         26.875   0.7087379   0.7654028 0.7811278
## 2 2         26.875   0.6796117   0.7464455 0.7694980
## 3 3         26.875   0.6796117   0.7630332 0.7762849
## 4 4         26.875   0.6990291   0.7677725 0.7731445
## 5 5         25.625   0.7087379   0.7085308 0.7640800


ROC: HHIES and HA adoption

Complete cases only (n=512)
Imputed data (n=525)
##   m best_threshold sensitivity specificity       auc
## 1 1              9   0.7475728    0.563981 0.6803249
## 2 2              9   0.7378641    0.563981 0.6737680
## 3 3              9   0.7378641   0.5687204 0.6774375
## 4 4              9   0.7475728   0.5687204 0.6821539
## 5 5              9   0.7378641    0.563981 0.6734574


ROC: SSQ-15i and HA adoption

Complete cases only (n=455)
Imputed data (n=525)
##   m best_threshold sensitivity specificity       auc
## 1 1       2.156667   0.6893204   0.3838863 0.5199351
## 2 2       2.156667   0.6990291   0.3767773 0.5222128
## 3 3       1.886667    0.631068   0.4336493 0.5233516
## 4 4       2.156667   0.6893204   0.3815166 0.5196475
## 5 5       2.156667   0.7087379   0.3838863 0.5267450


4. Special populations

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The standard relationship, HA ~ BPTA4

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Plots showing thresholds for BPTA4, Asymmetry, HHIES


  • Of the three, BPTA4 is the best standalone predictor of HA adoption.
  • Legend: Red = HA adopters. Lines are thresholds for highest area-under-curve. Complete cases only, n=423.

Comparing three predictors: BPTA4, Asymmetry, HHIES


  • On their own, BPTA4 and HHIES help predict HA adoption. On its own, PTA4 asymmetry doesn’t.
  • When BPTA4 is the main predictor, adding HHIES doesn’t help predict HA adoption, while adding PTA4 asymmetry does help a little.
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ 1
## Model 2: study2_HA ~ BPTA4
##   Resid. Df Resid. Dev Df Deviance  Pr(>Chi)    
## 1       422     413.17                          
## 2       421     336.89  1   76.272 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ 1
## Model 2: study2_HA ~ PTA4_asym
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       422     413.17                       
## 2       421     409.65  1   3.5179  0.06071 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ 1
## Model 2: study2_HA ~ HHIES_total
##   Resid. Df Resid. Dev Df Deviance    Pr(>Chi)    
## 1       422     413.17                            
## 2       421     392.72  1   20.448 0.000006129 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ BPTA4
## Model 2: study2_HA ~ BPTA4 + PTA4_asym
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       421     336.89                       
## 2       420     331.60  1   5.2977  0.02135 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:
## glm(formula = study2_HA ~ BPTA4 + PTA4_asym, family = "binomial", 
##     data = compdata)
## 
## Coefficients:
##              Estimate Std. Error z value           Pr(>|z|)    
## (Intercept) -4.617386   0.470057  -9.823            < 2e-16 ***
## BPTA4        0.119007   0.015530   7.663 0.0000000000000182 ***
## PTA4_asym    0.022451   0.009219   2.435             0.0149 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 413.17  on 422  degrees of freedom
## Residual deviance: 331.60  on 420  degrees of freedom
## AIC: 337.6
## 
## Number of Fisher Scoring iterations: 5
## Analysis of Deviance Table
## 
## Model 1: study2_HA ~ BPTA4
## Model 2: study2_HA ~ BPTA4 + HHIES_total
##   Resid. Df Resid. Dev Df Deviance Pr(>Chi)  
## 1       421     336.89                       
## 2       420     333.79  1   3.1032  0.07814 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:
## glm(formula = study2_HA ~ BPTA4 + HHIES_total, family = "binomial", 
##     data = compdata)
## 
## Coefficients:
##             Estimate Std. Error z value         Pr(>|z|)    
## (Intercept) -4.52791    0.46182  -9.804          < 2e-16 ***
## BPTA4        0.10849    0.01569   6.915 0.00000000000469 ***
## HHIES_total  0.02771    0.01568   1.768           0.0771 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 413.17  on 422  degrees of freedom
## Residual deviance: 333.79  on 420  degrees of freedom
## AIC: 339.79
## 
## Number of Fisher Scoring iterations: 5


“Red flag” variables

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Using BPTA4 as the standalone predictor of HA adoption, the sample can be divided into four groups:

##          predicted HA
## actual HA   0   1
##         0 280  85
##         1  23  61


The plot below shows potential “red flag” variables, and which individual participants have them within each group.

Continuous and ordinal variables have been dichotomized according to these cut-offs:
* PTA4 asymmetry ≥ 20 dB HL
* HHIES ≥ 10
* PHQ4 subscores ≥ 3
* Social participation of less than once per week in any activity
* Mean social support of less than “some of the time” (< 2.5 out of 5 on average)
* Generally, any WHOQOL-BREF responses that are in the worst 2 of 5 categories. There are a few exceptions, where it’s clear that the worst 3 categories are red flags according to the distribution (physical pain, medical treatment, money, information, getting around, health services, transport, negative mood).

Counts of participants experiencing each red flag
## [1] "Test of proportions conducted for first two columns: HA expected and nonHA unexpected"
## [1] "Test of proportions generally requires 5 positive cases per group"
##                  Variable HA_exp nonHA_unexp nonHA_exp HA_unexp  chisq pvalue
## 1           Asymmetry_bin      2           5         8        4 0.1112 0.7387
## 2               HHIES_bin     42          46        95       16 2.6342 0.1046
## 3    Tinnitus_past_wk_bin     15          35        82       10 3.6334 0.0566
## 4      Mobility_needs_bin      5           4        14        1 0.2664 0.6058
## 5   Poor_aided_vision_bin      3           1         8        0 0.7258 0.3942
## 6        positive_SCI_bin      7          11        25        4 0.0001 0.9916
## 7            PHQ4_anx_bin     26          23       100       11 3.1917 0.0740
## 8            PHQ4_dep_bin     11          23        74        7 1.1537 0.2828
## 9              Lonely_bin      9          19        52        7 0.8782 0.3487
## 10        MOS_socsupp_bin      3          11        10        4 1.7926 0.1806
## 11   CCHS_socpartfreq_bin      2           4        13        2 0.0000 0.9954
## 12            WHO_qol_bin      4           4         5        0 0.0135 0.9075
## 13  WHO_health_satisf_bin      7          16        32        4 0.9442 0.3312
## 14      WHO_phys_pain_bin      9          21        57        5 1.5879 0.2076
## 15  WHO_med_treatment_bin      8          18        51        2 1.0742 0.3000
## 16     WHO_enjoy_life_bin      1           5         5        1 0.7244 0.3947
## 17     WHO_meaningful_bin      3           6        11        0 0.0330 0.8559
## 18    WHO_concentrate_bin      2           3         6        1 0.0000 1.0000
## 19      WHO_feel_safe_bin      1           2         3        0 0.0000 1.0000
## 20    WHO_healthy_env_bin      2           1         1        0 0.0851 0.7705
## 21         WHO_energy_bin      3           6        13        2 0.0330 0.8559
## 22    WHO_body_appear_bin      2           7        14        2 0.7732 0.3792
## 23          WHO_money_bin      8          22        41        4 2.8071 0.0938
## 24    WHO_information_bin      5           6        11        0 0.0000 1.0000
## 25        WHO_leisure_bin      1           7        13        2 1.8456 0.1743
## 26     WHO_get_around_bin      2           5        11        2 0.1112 0.7387
## 27   WHO_sleep_satisf_bin     11          21        57        8 0.5753 0.4482
## 28    WHO_ability_ADL_bin      3           5        12        0 0.0000 1.0000
## 29  WHO_capacity_work_bin      4           5        21        1 0.0000 1.0000
## 30    WHO_satisf_self_bin      2           6        16        2 0.3859 0.5345
## 31   WHO_satisf_relat_bin      2          11        12        2 2.9833 0.0841
## 32     WHO_satisf_sex_bin     13          19        60        4 0.0000 1.0000
## 33 WHO_satisf_support_bin      1           4         9        1 0.2954 0.5868
## 34   WHO_living_place_bin      4           6         8        3 0.0000 1.0000
## 35  WHO_access_health_bin      6          10        39        3 0.0099 0.9209
## 36      WHO_transport_bin      0           3        13        3 0.7942 0.3728
## 37   WHO_neg_feelings_bin      9          15        45        4 0.0570 0.8113
## 38      Motiv_convers_bin      9           8        25        0 0.5343 0.4648
## 39         Motiv_lect_bin     11          15        34        2 0.0000 1.0000
## 40      Motiv_tvradmu_bin      9          17        26        2 0.3574 0.5500
## 41       Motiv_family_bin      5           8        12        0 0.0000 1.0000
## 42      Motiv_friends_bin     11           9        12        1 1.0947 0.2954
## 43       Motiv_social_bin     12           7        22        1 3.1554 0.0757
## 44      Motiv_sadfrus_bin     14          12        23        5 1.3377 0.2474
## 45      Motiv_fatigue_bin     20          19        38        2 1.4779 0.2241
## 46       Motiv_health_bin     15          22        43        5 0.0000 1.0000
## 47         Motiv_cogn_bin     14          19        27        4 0.0000 1.0000
Percentages of participants experiencing each red flag
## [1] "Test of proportions conducted for first two columns: HA expected and nonHA unexpected"
## [1] "Test of proportions generally requires 5 positive cases per group"
##                  Variable HA_exp_p nonHA_unexp_p nonHA_exp_p HA_unexp_p  chisq pvalue
## 1           Asymmetry_bin      3.3           5.9         2.9       17.4 0.1112 0.7387
## 2               HHIES_bin     68.9          54.1        33.9       69.6 2.6342 0.1046
## 3    Tinnitus_past_wk_bin     24.6          41.2        29.3       43.5 3.6334 0.0566
## 4      Mobility_needs_bin      8.2           4.7         5.0        4.3 0.2664 0.6058
## 5   Poor_aided_vision_bin      4.9           1.2         2.9        0.0 0.7258 0.3942
## 6        positive_SCI_bin     11.5          12.9         8.9       17.4 0.0001 0.9916
## 7            PHQ4_anx_bin     42.6          27.1        35.7       47.8 3.1917 0.0740
## 8            PHQ4_dep_bin     18.0          27.1        26.4       30.4 1.1537 0.2828
## 9              Lonely_bin     14.8          22.4        18.6       30.4 0.8782 0.3487
## 10        MOS_socsupp_bin      4.9          12.9         3.6       17.4 1.7926 0.1806
## 11   CCHS_socpartfreq_bin      3.3           4.7         4.6        8.7 0.0000 0.9954
## 12            WHO_qol_bin      6.6           4.7         1.8        0.0 0.0135 0.9075
## 13  WHO_health_satisf_bin     11.5          18.8        11.4       17.4 0.9442 0.3312
## 14      WHO_phys_pain_bin     14.8          24.7        20.4       21.7 1.5879 0.2076
## 15  WHO_med_treatment_bin     13.1          21.2        18.2        8.7 1.0742 0.3000
## 16     WHO_enjoy_life_bin      1.6           5.9         1.8        4.3 0.7244 0.3947
## 17     WHO_meaningful_bin      4.9           7.1         3.9        0.0 0.0330 0.8559
## 18    WHO_concentrate_bin      3.3           3.5         2.1        4.3 0.0000 1.0000
## 19      WHO_feel_safe_bin      1.6           2.4         1.1        0.0 0.0000 1.0000
## 20    WHO_healthy_env_bin      3.3           1.2         0.4        0.0 0.0851 0.7705
## 21         WHO_energy_bin      4.9           7.1         4.6        8.7 0.0330 0.8559
## 22    WHO_body_appear_bin      3.3           8.2         5.0        8.7 0.7732 0.3792
## 23          WHO_money_bin     13.1          25.9        14.6       17.4 2.8071 0.0938
## 24    WHO_information_bin      8.2           7.1         3.9        0.0 0.0000 1.0000
## 25        WHO_leisure_bin      1.6           8.2         4.6        8.7 1.8456 0.1743
## 26     WHO_get_around_bin      3.3           5.9         3.9        8.7 0.1112 0.7387
## 27   WHO_sleep_satisf_bin     18.0          24.7        20.4       34.8 0.5753 0.4482
## 28    WHO_ability_ADL_bin      4.9           5.9         4.3        0.0 0.0000 1.0000
## 29  WHO_capacity_work_bin      6.6           5.9         7.5        4.3 0.0000 1.0000
## 30    WHO_satisf_self_bin      3.3           7.1         5.7        8.7 0.3859 0.5345
## 31   WHO_satisf_relat_bin      3.3          12.9         4.3        8.7 2.9833 0.0841
## 32     WHO_satisf_sex_bin     21.3          22.4        21.4       17.4 0.0000 1.0000
## 33 WHO_satisf_support_bin      1.6           4.7         3.2        4.3 0.2954 0.5868
## 34   WHO_living_place_bin      6.6           7.1         2.9       13.0 0.0000 1.0000
## 35  WHO_access_health_bin      9.8          11.8        13.9       13.0 0.0099 0.9209
## 36      WHO_transport_bin      0.0           3.5         4.6       13.0 0.7942 0.3728
## 37   WHO_neg_feelings_bin     14.8          17.6        16.1       17.4 0.0570 0.8113
## 38      Motiv_convers_bin     14.8           9.4         8.9        0.0 0.5343 0.4648
## 39         Motiv_lect_bin     18.0          17.6        12.1        8.7 0.0000 1.0000
## 40      Motiv_tvradmu_bin     14.8          20.0         9.3        8.7 0.3574 0.5500
## 41       Motiv_family_bin      8.2           9.4         4.3        0.0 0.0000 1.0000
## 42      Motiv_friends_bin     18.0          10.6         4.3        4.3 1.0947 0.2954
## 43       Motiv_social_bin     19.7           8.2         7.9        4.3 3.1554 0.0757
## 44      Motiv_sadfrus_bin     23.0          14.1         8.2       21.7 1.3377 0.2474
## 45      Motiv_fatigue_bin     32.8          22.4        13.6        8.7 1.4779 0.2241
## 46       Motiv_health_bin     24.6          25.9        15.4       21.7 0.0000 1.0000
## 47         Motiv_cogn_bin     23.0          22.4         9.6       17.4 0.0000 1.0000